My remembering of a standard exposition (found the source, see edit) goes like this: a beautiful waterfall is a complicated dynamic system, containing many more atoms than a human brain, all in motion. Were one clever, one could map the motion of water in part of the waterfall to motion of atoms and charge in a human brain. Then the waterfall is a person, thinking thoughts as it burbles. Except there is a problem, where each waterfall has many possible mappings, and thus spans the whole range of brains!

If one then asks the question "so why aren't you a waterfall?" this is a sort of epistemological analogue to the Boltzmann brain hypothesis.

I seem to recall the original argument going a different place: "are waterfalls on-average blissful or suffering, and by how much do billions of waterfalls encoding all possible minds outweigh our petty human concerns?"

EDIT: Ah, found the source (ctrl+f "waterfall"), which references Putnam and Searle, and is worth a read in its entirety. A little discussion of ethical implications on LW can be found here.